Which of the following numbers is a factor of 70? ${4,6,10,11,13}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $70$ by each of our answer choices. $70 \div 4 = 17\text{ R }2$ $70 \div 6 = 11\text{ R }4$ $70 \div 10 = 7$ $70 \div 11 = 6\text{ R }4$ $70 \div 13 = 5\text{ R }5$ The only answer choice that divides into $70$ with no remainder is $10$ $ 7$ $10$ $70$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $10$ are contained within the prime factors of $70$ $70 = 2\times5\times7 10 = 2\times5$ Therefore the only factor of $70$ out of our choices is $10$. We can say that $70$ is divisible by $10$.